当前位置:首页 >> 机械/仪表 >>

Radial basis function


Radial basis function
From Wikipedia, the free encyclopedia

A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that a center, so that ; or alternatively on the distance from some other point c, called . Any function φ that satisfies the property is aradial function. The

norm is usually Euclidean distance, although other distance functions are also possible. For example by using Lukaszyk-Karmowski metric, it is possible for some radial functions to avoid problems with ill conditioning of the matrix solved to determine coefficients wi (see below), since the is always greater than zero.[1]

Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind ofneural network.
Contents [hide]

1 RBF types 2 Approximation 3 RBF network 4 References

[edit]RBF

types

Commonly used types of radial basis functions include (writing

):

Gaussian:

Multiquadric:

Polyharmonic spline:

Thin plate spline (a special polyharmonic spline):

[edit]Approximation

Radial basis functions are typically used to build up function approximations of the form

where the approximating function y(x) is represented as a sum ) of N radial basis functions, each associated with a different center ci, and weighted by an appropriate coefficient wi. The weights wi can be estimated using the matrix methods of linear least squares because squares, the approximating function is islinear in the weights. Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple simplechaotic behaviour, 3D reconstruction in computer graphics (for example, hierarchical RBF).

[edit RBF edit]

network

See also: radial basis function network

Two unnormalized Gaussian radial basis functions in one input dimension. The basis function centers are located at c1=0.75 and c2=3.25.

The sum

can also be interpreted as a rather simple single-layer type of artificial neural network called aradial basis function network, with the radial basis functions taking on the role of the activation functions of the network. It can be shown that any continuous function on a compact interval can in principle be interpolated with arbitrary accuracy by a sum of this form, if a sufficiently large number N of radial basis functions is used. The approximant y(x) is differentiable with respect to the weights wi. The weights could thus be learned using any of the standard iterative methods for neural networks.

[edit]References

1.

^ Lukaszyk, S. (2004) A new concept of probability metric and its applications in approximation of scattered data sets. Computational Mechanics, 33, 299-3004. limited access

Buhmann, Martin D. (2003), Radial Basis Functions: Theory and Implementations, Cambridge University Press, ISBN 978-0-521-63338-3. Categories: Neural networks | Interpolation | Numerical analysis

V


相关文章:
科技论文英语
They used the radial basis function (Radial Basis Function, RBF) neural network technology, the flash point and boiling point of 400 kinds of organic ...
Surfer---九种插值方法
Radial Basis Function--径向基函数法 Triangulation with Linear Interpolation--线性插值三角网法 Moving Average--移动平均法 Local Polynomial--局部多项式法 1、 ...
VC basis configuration
Radial basis function ... 暂无评价 19页 免费 Configuration Manageme... ...VC Basis configuration VC Flex-10 VC 1/10GB ethernet VC 4GB FC VC 8GB ...
神经网络elm算法
basis function % 'radbas' for Radial basis function (for additive type of SLFNs instead of RBF type of SLFNs) % % Output: % TrainingTime - Time ...
智能信息处理重点总结
(Radial basis function) SOM网络:Self -Orginazing Maps network 自组织网络 /*了解 旅行商问题(TSP, traveling salesman problem) 知识库(Knowledge Base) 下...
高斯(核)函数简介
高斯(核)函数简介 1 函数的基本概念 所谓径向基函数 (Radial Basis Function 简称 RBF), 就是某种沿径向对称的标量函数。 通常定 义为空间中任一点 x 到某一...
反问题参考书目
Powell, The Theory of Radial Basis Function Approximation in 1990, preprint. 29. Robert Dautray, Jacques-Louis Lions, Mathematical Analysis and Numerical ...
SVM参数说明
set type of kernel function (default 2) 0 -- linear: u'*v 1 -- polynomial: (gamma*u'*v + coef0)^degree 2 -- radial basis function: exp(...
随机过程
function (Poly)tests than radial basis function(RBF),so that the model has high accuracy and generalization ability.The signal can be given to achieve ...
商务智能实验
(gamma*u'*v + coef0)^degree\n" + "\t\t 2 = radial basis function: exp(-gamma*|u-v|^2)\n" + "\t\t 3 = sigmoid: tanh(gamma*u'*v ...
更多相关标签: